November 27, 2020

The first space launch occurred October 4, 1957. What was its name and who launched it?

One month later, on November 3, 1957, the first living being was launched into space. What was the name of this first cosmonaut?

It took four more years (and over 30 cosmo-dogs) before the first human was launched into space on April 12, 1961.

And then another eight years for humans to set foot on our Moon on July 20, 1969.

Project Goal

  • Determine the relationship between Space Mission Success and other variables

Space Shuttle Challenger exploded moments after launching on January 28, 1986. Source: CNN news

Data


Source: https://www.kaggle.com/agirlcoding/all-space-missions-from-1957

EDA

EDA

Method

  • Categorical Data Analysis with Logistic Regression \[\displaystyle logit(\pi) = log \left( \frac{\pi}{1- \pi} \right) = \beta_0 + \beta_1 X_{1} + \beta_2 X_{2} + \ldots + \beta_k X_{k}\]

  • Single Logistic Regression models \[\displaystyle logit(\pi) = log \left( \frac{\pi}{1- \pi} \right) = \beta_0 + \beta_1 X_{1}\]

    • Response variable: Mission Outcome (Success: Yes/No)

    • Predictors: Rocket Status (Active/Retired), Country (USA/Russia), Space Race Decade (1960s/1970s)

Inferences

  • Hypothesis test for the slope
    • Test whether the groups/levels in the explanatory variable differ in chance (odds) of success

\(H_o:\) \(\beta_1 = 0\)

\(H_a:\) \(\beta_1 \ne 0\)

Test statistic: \(\displaystyle z = \frac{\hat{\beta_1}}{s(\hat{\beta_1})}\)

p-value = 2*pnorm(z, lower.tail = FALSE)

  • Confidence interval

\[\hat{\beta_1} \pm z_{({1 - \alpha/2})} s(\hat{\beta_1})\]

Mission Status vs Rocket Status

  • Is there a difference in the chance of success between active and retired rockets?

Mission Status vs Rocket Status

  • Model \[logit(Pr(Success)) = 2.084 + 0.528 \cdot Active\]
             Estimate Std. Error   z value    Pr(>|z|)
(Intercept) 2.0842255 0.05362567 38.866192 0.000000000
ActiveYes   0.5280206 0.15084041  3.500525 0.000464343
  • Untransform (exponentitate) slope to get odds ratio
ActiveYes     2.5 %    97.5 % 
 1.695573  1.272852  2.301764

USA vs Russia

  • Do the two countries have the same chance of space mission success?

USA vs Russia

  • Model \[logit(Pr(Success)) = 2.016 + 0.319 \cdot Russia\]
              Estimate Std. Error  z value Pr(>|z|)
(Intercept)    2.01575    0.08469 23.80166  0.00000
CountryRussia  0.31928    0.11446  2.78945  0.00528
  • Inferences
CountryRussia                       2.5 %        97.5 % 
    1.3761360     0.5791487     1.0988476     1.7216396

Space Race Decades: 1960s and 1970s

Apollo 11

Space Race Decades: 1960s and 1970s

  • Do the two decades differ in terms of successful rate of space mission?

Space Race Decades: 1960s and 1970s

  • Model \[logit(Pr(Success)) = 1.329 + 1.211 \cdot Decade1970s\]

  • Inferences

Decade1970s       2.5 %      97.5 % 
   3.355326    2.512054    4.519424

Which model gives us best prediction?

  • AIC (Akaike’s Information Criterion)

  • The smaller the AIC, the better the model

Summary

  • Active rockets have greater chance of success than retired rockets

(OR = 1.696, 95% CI (1.273, 2.302))

  • Russia is more likely to have successful space missions than USA

(OR = 1.376, 95% CI (1.099, 1.722))

  • There’s an increase in success rate from 1960s to 1970s

(OR = 3.355, 95% CI (2.512, 4.519))

Future Work

  • Time Series Analysis
  • Mixed Models
  • Spatial Visualization

Thanks!